•A global intercomparison of fifteen clear-sky irradiance models is proposed.•A common gridded hourly input database spanning one year is used.•Larger inter-model discrepancies found in direct irradiance than in global irradiance.•The highest differences found in Asia, Middle East and central and northern Africa.•Modeling improvements required for situations with high aerosol load. Clear-sky irradiance (CSI) modeling constitutes an essential component of the evaluation of the solar resource at any location, and is involved in a large number of applications. In solar applications, most common CSI models provide broadband irradiance predictions based on a number of simplifications and/or empirical components compared to the rigorous radiative transfer models used in atmospheric sciences. Thus, these common CSI models have to undergo continuous quality assurance evaluations to delineate the range of validity of such simplifications. Traditionally, these evaluations have consisted in direct comparisons against high-quality ground observations. A review of 36 such validation studies of the literature is provided here, highlighting which CSI models were recommended over different climatic areas. This review underlines the difficulty of generalizing these results due to a number of methodological difficulties. In particular, the availability of ground observations is limited and does not cover the full extent of the atmospheric conditions over which the CSI models are regularly operated. In this review study, fifteen of the most highly cited CSI models of the literature are compared to each other using a global synthetic input database built from atmospheric reanalyses. It guarantees that most of the operating conditions of CSI models are potentially covered. The study focuses on the global horizontal (GHI) and direct normal (DNI) irradiance predictions of the CSI models. Overall, a better agreement for GHI than for DNI is found. The largest inter-model discrepancies span throughout Asia, the Middle East and central and northern Africa, precisely coinciding with some of the regions with the highest interest for solar energy applications. The most important sources of discrepancies are traced down to high loads of aerosols, high site elevations, and low solar altitudes. Usage of the Linke turbidity factor as input to a popular type of simplified CSI model is found to be a significant source of uncertainty, preventing accurate simultaneous predictions of GHI and DNI. Other models, which tend to mispredict GHI or DNI over, e.g., hazy areas, are identified.